Parameter  Value  Ref. / Comments 

τ(B_{d})  (1.536 ± 0.014) ps  HFAG  Oscillations/Lifetime (Winter 2004) 
Δm_{d}  (0.502 ± 0.007) ps^{–1}  HFAG  Oscillations/Lifetime (Winter 2004) 
A_{^}^{ 2}  0.160 ± 0.032 ± 0.014  BABAR, PRL 87 (2001) 241801 
0.192 ± 0.023 ± 0.026  Belle, PL B538 (2002) 1120  
0.176 ± 0.025  Average used for rescaling 
Parameter: sin(2β/φ_{1}) (if β/φ_{1} dominant weak phase)  

Mode  BABAR  Belle  Average  Ref. / Comments 
J/ψK_{S}, ψ(2S)K_{S}, χ_{c1}K_{S}, η_{C}K_{S}  0.76 ± 0.07_{stat}  0.73 ± 0.06_{stat}    BABAR PRL 89 (2002) 201802 BelleCONF0353, LP'03 (preliminary) 
J/ψK_{L} (η_{CP}=+1)  0.72 ± 0.16_{stat}  0.80 ± 0.13_{stat}  
J/ψK*^{0} (K*^{0} → K_{S}π^{0}  0.22 ± 0.52_{stat}  0.10 ± 0.45_{stat}  
All charmonium  0.741 ± 0.067 ± 0.034  0.733 ± 0.057 ± 0.028 
0.736 ± 0.049 (0.043_{statonly}) 
CL = 0.93 
ΦK^{0}  0.47 ± 0.34 ^{+0.08}_{–0.06}  –0.96 ± 0.50 ^{+0.09}_{–0.11}  0.02 ± 0.29
(0.28_{statonly}) CL=0.021 
BABAR hepex/0403026 (submitted to PRL) BABAR PRL 91 (2003) 161801 PRL 91, 261602 (2003) BABAR MoriondEW (2004) (preliminary) 
η'K_{S}  0.02 ± 0.34 ± 0.03  0.43 ± 0.27 ± 0.05  0.27 ± 0.21
(0.21_{statonly}) CL=0.35 

f_{0}K_{S}  1.62 ^{+0.51}_{–0.56} ± 0.10  not yet available  1.62 ^{+0.51}_{–0.56} ± 0.10  
π^{0}K_{S}  0.48 ^{+0.38}_{–0.47} ± 0.11  not yet available  0.48 ^{+0.38}_{–0.47} ± 0.11  
K^{+}K^{–}K_{S}  0.56 ± 0.25 ± 0.04 ^{+0.17}_{–0.00}  0.51 ± 0.26 ± 0.05 ^{+0.18}_{–0.00}  0.54 ± 0.18 ^{+0.17}_{–0.00}
(0.18_{statonly}) CL=0.89 

All b → s penguin  0.42 ± 0.12 (0.12_{statonly})  CL = 0.03  
All modes  0.690 ± 0.045 (0.41_{statonly})  CL = 0.0088 
Parameter: sin(2β/φ_{1})  

Experiment  Value  Ref. / Comments  
ALEPH  0.84 ^{+0.82}_{–1.04} ± 0.16  PL B492 (2000) 259274  
OPAL  3.2 ^{+1.8}_{–2.0} ± 0.5  EPJ C5 (1998) 379388  
CDF (full Run I)  0.79 ^{+0.41}_{–0.44}(stat+syst)  PRD 61 (2000) 072005 
Parameter: sin(2β/φ_{1})  

All charmonium  0.739 ± 0.048  
All modes  0.692 ± 0.045 
Parameter: C=–A (if not stated otherwise)  

Mode  BABAR  Belle  Average  Ref. / Comments 
Charmonium  λ = 0.948 ± 0.051 ± 0.030 
0.950 ± 0.049 ± 0.034 (added DCSD systematics) 
0.949 ± 0.045 (0.035_{statonly}) CL = 0.98 
BABAR PRL 89 (2002) 201802 Belle PRD 66 (2002) 071102 
C = 0.053 ^{+0.055}_{–0.052} ^{+0.032}_{–0.031} 
0.051 ^{+0.053}_{–0.050}
^{+0.035}_{–0.036} (added DCSD systematics) 
0.052 ^{+0.048}_{–0.046}
(0.037_{statonly})
CL = 0.98 

ΦK_{S}  0.01 ± 0.33 ± 0.10  0.15 ± 0.29 ± 0.08 (added DCSD systematics) 
0.09 ± 0.23 CL=0.76 
BABAR hepex/0403026 (submitted to PRL) BABAR PRL 91 (2003) 161801 PRL 91, 261602 (2003) BABAR MoriondEW (2004) (preliminary) 
η'K_{S}  0.10 ± 0.22 ± 0.04 (added DCSD systematics) 
0.01 ± 0.16 ± 0.05 (added DCSD systematics) 
0.04 ± 0.13 CL=0.75 

f_{0}K_{S}  0.27 ± 0.36 ± 0.12  not yet available  0.27 ± 0.36 ± 0.12  
π^{0}K_{S}  0.40 ^{+0.27}_{–0.28} ± 0.10  not yet available  0.40 ^{+0.27}_{–0.28} ± 0.10  
K^{+}K^{–}K_{S}  –0.10 ± 0.19 ± 0.09  0.17 ± 0.16 ± 0.05 (added DCSD systematics) 
0.07 ± 0.13 CL=0.31 

All b → s penguin  0.09 ± 0.08 (0.08_{statonly})  CL = 0.92  
All modes  0.059 ± 0.039 (0.033_{statonly})  CL = 0.97 
Constraining C_{J/ψ Ks}
from A_{CP}(B^{+} → J/ψ K^{+})
and A_{SL}: as suggested by
Y. Nir,
one can obtain a powerful SM constraint on
λ = q/pAbar/A via the relations
A_{SL} = (1–q/p^{4})/(1+q/p^{4})
and
A_{CP}(B^{+} → J/ψ K^{+})
= (Abar/A^{2}–1)/(Abar/A^{2}+1),
where A_{SL} denotes the CP asymmetry in semileptonic
B decays,
and A_{CP}(B^{+} → J/ψ K^{+})
is the CPviolating charge asymmetry measured in
B^{+} → J/ψ K^{+} decays.
Averaging the A_{SL} results from
BABAR,
CLEO,
ALEPH and
OPAL,
as well as the A_{CP}(B^{+} → J/ψ K^{+})
results from
BABAR,
Belle and
CLEO,
we find
A_{SL} = 0.001 ± 0.014 and
A_{CP}(B^{+} → J/ψ K^{+})
= –0.007 ± 019. This
gives
q/p = 0.9996 ^{+0.0068 }_{–0.0067},
Abar/A = 0.993 ± 0.018,
and hence
λ_{indirect} = 0.992 ± 0.019
(see right hand plot below).
Discussion: the amplitude relation between neutral and charged B → J/ψ K decays has been found by FleischerMannel to hold up to negligible corrections of the order O(λ^{3}). However, it was pointed out by D. Kirkby that the identification of λ, measured through the C coefficient in B^{0} → J/ψ K^{0}, with q/pAbar/A assumes ΔΓ_{Bd}=0. The ratio ΔΓ_{Bd}/Δm_{Bd} it is expected to be small in the SM. 
Compilation of results for –ηS ≈ sin(2β/φ_{1}) and C (the two right hand plots show averages) 
eps gif gif(high res) 
eps gif gif(high res) 
eps gif gif(high res) 
Constraining the Unitarity Triangle (ρ, η):
the measurement of sin(2β) from charmonium modes
can be compared in the ρbarηbar plane (ρbar, ηbar being the
parameters in the exact (unitary)
Wolfenstein
parameterization of the CKM matrix) with the constraints from
other experimental inputs. Visit the CKMfitter homepage and the UTfit homepage for results on global CKM fits using different fit techniques and input quantities. 
Experiment  S_{J/ψπ0}  C_{J/ψπ0} = –A_{J/ψπ0}  Correlation  Ref. / Comments  

BABAR'02 N(BB)=88m 
0.05 ± 0.49 ± 0.16  0.38 ± 0.41 ± 0.09  –0.12  PRL 91 (2003) 061802  
Belle'03 N(BB)=151m 
–0.72 ± 0.42 ± 0.08  0.01 ± 0.29 ± 0.07  –0.12  Belle CONF0342 (LP'03)  
Average (preliminary) 
–0.40 ± 0.33  0.13 ± 0.24  –0.12  χ^{2} = 2.1 (CL = 0.36 → 0.9σ)  
eps gif gif (high res) 
eps gif gif (high res) 
nothing 
Experiment  S_{D*+D*–}  C_{D*+D*–}  Correlation  Ref. / Comments  

BABAR'03 N(BB)=88m 
Im(λ) = 0.05 ± 0.29 ± 0.10  λ = 0.75 ± 0.19 ± 0.02  0.18 
PRL 91 (2003) 131801 f(CPodd) = 0.063 ± 0.055 ± 0.009 

S = 0.06 ± 0.37 ± 0.13  C = 0.28 ± 0.23 ± 0.02  –0.15  
Belle  not yet available 
Experiment  S_{+–}(D*^{+}D^{–})  C_{+–}(D*^{+}D^{–})  S_{–+}(D*^{–}D^{+})  C_{–+}(D*^{–}D^{+})  A_{+–}  Ref. / Comments 

BABAR'03 N(BB)=89m 
–0.82 ± 0.75 ± 0.14  –0.47 ± 0.40 ± 0.12  –0.24 ± 0.69 ± 0.12  –0.22 ± 0.37 ± 0.10  –0.03 ± 0.11 ± 0.05  PRL 90 (2003) 221801 
Belle  not yet available 
Compilation of results for sin(2β_{eff}/φ_{1,eff})=–S (left figure) and C (right figure) from timedependent b → ccbar d analyses. The results are compared to the values from the corresponding charmonium averages. 
eps gif gif(high res) 
eps gif gif(high res) 
Experiment  S_{ππ}  C_{ππ} = –A_{ππ}  Correlation  Ref. / Comments  

BABAR'03 N(BB)=123m 
–0.40 ± 0.22 ± 0.03  –0.19 ± 0.19 ± 0.05  –0.02  BABARPlot0053 (preliminary)  
updated Winter'04: Belle'04 N(BB)=152m 
–1.00 ± 0.21 ± 0.07  –0.58 ± 0.15 ± 0.07  –0.286  hepex/0401029  
Average  –0.74 ± 0.16  –0.46 ± 0.13  –0.17  χ^{2} = 6.9 (CL = 0.031 → 2.2σ)  
eps gif gif (high res) 
eps gif gif (high res) 
nothing 
The Penguintotree ratio:
using as input the measured
C_{ππ} and S_{ππ} coefficients
together with the Wolfenstein parameters ρ and η from
the Global CKM fit
using standard constraints,
one can infer module and phase of the complex penguin
to tree (P/T) ratio
in B_{d}→ π^{+}π^{–}
decays within the Standard Model. Note that the definition of P/T is
conventiondependent (see, e.g.,
GroRo02).
We choose to eliminate the charm quark in
the penguin loop using CKM unitarity, so that the amplitudes can be
parameterized as follows:

Experiment  A_{CP}(ρπ)  S_{ρπ}  C_{ρπ}  ΔS_{ρπ}  ΔC_{ρπ}  Correlations  Ref. / Comments 

BABAR'03 N(BB)=123m 
–0.114 ± 0.062 ± 0.027  –0.13 ± 0.18 ± 0.04  0.35 ± 0.13 ± 0.05  0.33 ± 0.18 ± 0.03  0.20 ± 0.13 ± 0.05  Table  LP'03 update: BABARPlot0055 (preliminary) 
Belle  not yet available 
Direct CP violation: as shown by
Charles
it is convenient to transform the experimentally motivated direct
CP parameters A_{CP}(ρπ) and C_{ρπ}
into the physically motivated A^{+–}(ρπ) = (κ^{+–}^{2}–1)/(κ^{+–}^{2}+1) = –(A_{CP}(ρπ)+C_{ρπ}+A_{CP}(ρπ)ΔC_{ρπ})/(1+ΔC_{ρπ} + A_{CP}(ρπ)C_{ρπ}), A^{–+}(ρπ) = (κ^{–+}^{2}–1)/(κ^{–+}^{2}+1) = (–A_{CP}(ρπ)+C_{ρπ}+A_{CP}(ρπ)ΔC_{ρπ})/(–1+ΔC_{ρπ} + A_{CP}(ρπ)C_{ρπ}), where κ^{+–}=(q/p)Abar^{–+}/A^{+–} and κ^{–+}=(q/p)Abar^{+–}/A^{–+}. With this definition A^{–+}(ρπ) (A^{+–}(ρπ)) describes direct CP violation in B_{d} decays where the ρ is emitted (not emitted) by the spectator interaction. Taking into account experimental correlations, one finds A^{+–}(ρπ) = –0.18 ± 0.13 ± 0.05, A^{–+}(ρπ) = –0.52 ^{+0.17}_{–0.19} ± 0.07, where the first errors are statistical and the second systematic. The two quantities are experimentally correlated to +51%. The probability to observe these numbers in the absence of direct CP violation is 1.5%. See right hand plot for a confidence level representation in the A^{+–}(ρπ) versus A^{–+}(ρπ) plane. 
eps gif gif (high res) 

Flavorcharge specific branching fractions: the charge and
flavor asymmetry parameters A_{CP}(ρπ), C_{ρπ} and
ΔC_{ρπ} can be used to derive flavorcharge specific
rates from the
HFAG branching fraction
BR(B_{d}→ ρ^{+–}π^{–+})=(24.0 ± 2.5) 10^{–6}.

Experiment  S_{long}  C_{long}  Correlation  Ref. / Comments 

BABAR'04 N(BB)=123m 
–0.19 ± 0.33 ± 0.11  –0.23 ± 0.24 ± 0.14  0.04  BABAR MoriondEW (2004) (preliminary) 
Belle  not yet available 
The Penguintotree ratio: using as input the measured C_{long} and S_{long} coefficients together with the Wolfenstein parameters ρ and η using standard constraints, one can infer module and phase of the complex penguin to tree (P/T) ratio as done in the ππ case. Plots for confidence level representations of the P/T phase versus its module can be found on the corresponding CKMfitter and UTfit pages. 
Constraining α: using as input the measured C_{long} and S_{long} coefficients together with the present (HFAG) ρρ branching fractions and longitudinal polarization fractions (including the limit on ρ^{0}ρ^{0}, for which the polarization is unknown), one can perform the GronauLondon isospin analysis (electroweak penguins can be taken into account, while other SU(2)breaking effects are usually neglected). Plots for confidence level representations of the P/T phase versus its module can be found on the corresponding CKMfitter and UTfit pages. 
Observable  BABAR  Belle  Average*  Ref. / Comments  

partially reconstructed 
fully reconstructed 
fully reconstructed 

a*  –0.063 ± 0.024 ± 0.014  –0.068 ± 0.038 ± 0.020  0.060 ± 0.040 ± 0.017 
–0.037 ± 0.021 CL=0.04 
BABAR hepex/0310037 (partial. rec., preliminary) (submitted to PRL) BABAR hepex/0309017 (fully rec., preliminary) (submitted to PRL) Belle hepex/0308048 (submitted to PRL) 
c*  –0.004 ± 0.037 ± 0.020
(lepton tags only) 
0.031 ± 0.070 ± 0.033
(lepton tags only) 
0.049 ± 0.040 ± 0.019 
0.022 ± 0.028 CL=0.68 

a    –0.022 ± 0.038 ± 0.020  –0.062 ± 0.037 ± 0.016 
–0.043 ± 0.029 CL=0.50 

c    0.025 ± 0.068 ± 0.033
(lepton tags only) 
–0.025 ± 0.037 ± 0.018 
–0.014 ± 0.036 CL=0.56 
Experiment  γ/φ_{3}  Ref. / Comments  

Belle'04 N(BB)=152m 
81° ± 19°(1σ*) ± 13° ± 11°_{model} 
Belle Lake Luise (2004) and Belle Moriond (2004) (preliminary) 

BABAR  not yet available 